momo
2012-02-13
Hello,
I have a problem: all of a polynomial real zero-finding.
The problem is as follows:
Be a Real polynomial p (x) = (am) * x ** m + (am-1) * x ** m-1 + …. + a1 * x + a0
with m = 2 * k and real parameters (Am. .. a0)
are all zeros of p (x) all real?
i.e. the output to be rlqe (by quantifier elimination) must be true or false!
I have tried to solve with realroots and r_solve but no success.
Thank you very much.
Thomas Sturm
2012-02-13
I do not quite understand you problem.
If you have got concrete coefficients, then you can use "realroots" and compare the number of roots found with the degree.
If you consider a generic problem with all the a_i being parameters, then you can for fixed degree m use real quantifier elimination on
ex({x1,...,xm}, x1<>x2 and x1<>x3 and ... and x_m-1<>x_m and p(x_1)=0 and ... and p(x_m)=0)
,
but for absolutely generic problems you will not get very far.
Thomas
momo
2012-02-13
Many thanks for your answer
my idea is:
If I have a polynomial of degree m and I m getting zero the real.
Then the problem is solved.
Only here is the problem that I work with general real parammetern
Thomas Sturm
2012-02-13
Quantifier elimination would give you necessary and sufficient conditions in the parameters. Can you post concrete input, and carefully formulate the question that you have on that input?
Thomas
momo
2012-02-13
Hallo Thomas,
Input : something real polynomial with parameters;
Output : all the real zero the polynomial
Thanks